The perimeter of the triangle ABC is 78 cm. Find the lengths of the sides of this triangle if AB: BC = 3: 4, and BC: AC = 2: 3.
Since we have two relations where the BC appears, we will express it:
BC = 4AB / 3, BC = 2AC / 3, equate the obtained expressions and get that AC = 2AB, it is convenient to rewrite everything through AB, but first we denote AB as x, then:
AB = x, AC = 2x, BC = 4x / 3, and our perimeter is 78 cm, then:
x + 2x + 4x / 3 = 78,
13x / 3 = 78,
13x = 234,
x = 18.
It follows from this that AB = 18 cm, AC = 36 cm, BC = 24 cm.
Answer: AB = 18 cm, AC = 36 cm, BC = 24 cm.
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